الفرق بين المراجعتين لصفحة: «نقاش:القرآن»
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To-- specify the connection it is enough to specify, for all i, j, and k, |
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We also recall that, locally, a connection is given by m3 smooth functions {Γlij}, where |
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The torsion-free property means |
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On the other hand, compatibility with the Riemannian metric implies that |
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For a fixed, i, j, and k, permutation gives 3 equations with 6 unknowns. The torsion free assumption reduces the number of variables to 3. Solving the resulting system of 3 linear equations gives unique solutions |
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This is the first Christoffel identity. |
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